Re: Concert Pitch (a second try)

[Hans Aberg]

On 7 Apr 2009, at 08:18, Peter Chubb wrote:

> Here's my rough try at the three entries:
>
> Concert Pitch:
> Notes like a, b, c etc., describe a relationship between themselves,
> not an absolute pitch.  The nature of the relationship is the
> so-called temperament (q.v.).  To be in tune, a group instruments  
> must agree
> on the relationship between pitches *and* the absolute pitch of one of
> the notes.  In recent times that pitch, `concert pitch' has been
> defined as 440Hz for the A above middle C, with other notes arranged
> according to the temperament being used.

The term "concert pitch", from what I looked up, can refer to two  
different concepts: a non-transposing instrument, and a tuning  
standard (like international A = 440 Hz).

I do not want to tie these concepts together, so that a transposing  
instrument is becomes one that uses different tuning, because the  
notational system is in fact more clever:

There is one set of notated pitches. All instruments must agree on  
these pitches, otherwise they will sound out of tune when playing  
together. This system of notated pitches are fixed by a tuning  
standard which is one note set at a specific frequency. The other  
notes in the notation system are set by choice of intonation. One  
generally does not know what the frequencies of those are, as the may  
be adjusted by musical context or stretch tuning.

> Transposing Instrument:  If an instrument is usually notated at a
> pitch other than its sounding pitch (whether out of tradition, or for
> the convenience of the player) it is said to be a *transposing
> instrument.*  Bes and A Clarinets, many brass instruments, and some  
> saxophones
> are transposing instruments.

Then a transposing instrument is simply one that plays a different  
pitch than the notated, but still in that notation system. The note  
will comes out right, as it is transposed twice in opposite  
directions: first by the composer who writes the sheet music, and then  
the musician who plays the instrument.

> Temperament: the relationship between different pitches in a scale.
> In the simplest case, an *equal-tempered* system has notes whose
> frequencies are in the ratio of the twelfth root of two.  Such a
> system always sounds out-of-tune, because thirds, fourths and fifths
> are not exact ratios.  However it is widely used because all notes are
> equally spaced, regardless of the starting note of a scale.

Yes, E12 (which is the Scala name for a 12-ET notational system) is a  
system that sounds equally bad in all keys :-). I think that  
historically E12 like tunings were used early on lutes, but during the  
Renaissance one used keyboards that approximated extended meantone  
tunings (where the major second is close to the interval sqrt(5/4)).  
If this is cut down to a meantone 12 keys per octave, it will have an  
interval jump somewhere called a "wolf" due to the fact it sounds very  
badly. The E12 keyboard solves that problem.

I have though used an extended meantone, or diatonic, keyboard layout  
with Scala on my computer typing keyboard for several months now. It  
works just fine playing in any key - as it is fully transposable,  
there is only one fingering to learn for each scale or chord  
regardless of key.

I might be usable for entering notes as well, as it does not apply E12  
enharmonic equivalence, as piano keyboards do.

  Hans